SOLUTION: The bottom of a box is supposed to be a rectangle with the perimeter of 36 cm. The box must be 4 cm high. what dimensions give the maximum volume?
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Question 224025: The bottom of a box is supposed to be a rectangle with the perimeter of 36 cm. The box must be 4 cm high. what dimensions give the maximum volume? Answer by drj(1380) (Show Source):
You can put this solution on YOUR website! The bottom of a box is supposed to be a rectangle with the perimeter of 36 cm. The box must be 4 cm high. what dimensions give the maximum volume?
Step 1. The maximum volume is when the rectangle is a square and let s be the side of the square.
Step 2. The perimeter P of a rectangle (or square) means adding up all four sides. So P=s+s+s+s=4s since all four sides of the square are equal.
Step 3. But P=36=4s. Solving for s=36/4=9 cm.
Step 4. Volume V=A*h of the box where A is the area of the square and h is the height given as h=4.
Step 5. Area for a square. So square centimeters.
Step 6. Then V=A*h=81*4=324 cubic centimeters.
Step 7. ANSWER: The maximum volume of the box is 324 cubic centimeters.
I hope the above steps and explanation were helpful.
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